Modularity in tangential k-blocks
type: Item
instance of: scholarly article
title: Modularity in tangential k-blocks
zbMATH Open document ID: 0578.05009
DOI: 10.1016/0095-8956(87)90060-8
author: Geoff Whittle
published in: Journal of Combinatorial Theory. Series B
publication date: 1987-01-01T00:00:00Z
review text: This paper examines the role of modularity in tangential k-blocks over GF(q). It is shown that if M is a tangential k-block over GF(q) and F is a modular flat of M which is affine over GF(q) then the simple matroid associated with the complete Brown truncation of M by F is also a tangential k-block over GF(q). This enables us to construct tangential k- blocks over GF(q) of all ranks r where \(q^ k-q+2\leq r\leq q^ k\). We also consider tangential k-blocks which have modular hyperplanes; bounds are placed on the rank of members of this class and some of their minors are exhibited.
Mathematics Subject Classification ID: 05B35
zbMATH DE Number: 3924790
zbMATH Keywords: modularity
zbMATH Keywords: tangential k-blocks
zbMATH Keywords: modular flat
zbMATH Keywords: matroid
zbMATH Keywords: complete Brown truncation
zbMATH Keywords: modular hyperplanes
MaRDI profile type: Publication
full work available at URL: 0095-8956(87)90060-8
OpenAlex ID: W2166799413
cites work: Q3050437
cites work: Modular Constructions for Combinatorial Geometries
cites work: Q3864533
cites work: Several identities for the characteristic polynomial of a combinatorial geometry
cites work: COLOURING, PACKING AND THE CRITICAL PROBLEM
cites work: On a matroid identity
cites work: Modular elements of geometric lattices
cites work: Supersolvable lattices
cites work: On the algebraic theory of graph colorings
cites work: Tangential 1-blocks over GF(3)
cites work: Q3898509
cites work: Matroids and block designs
cites work: Q4111952
description: scientific article; zbMATH DE number 3924790